Expand the Trigonometric Expression (-8a^2-1)(3a^2-5)

$(- 8 a^{2} - 1) (3 a^{2} - 5)$

Step 1

Expand $(- 8 a^{2} - 1) (3 a^{2} - 5)$ using the FOIL Method.

Apply the distributive property.

$- 8 a^{2} (3 a^{2} - 5) - 1 (3 a^{2} - 5)$

Apply the distributive property.

$- 8 a^{2} (3 a^{2}) - 8 a^{2} \cdot - 5 - 1 (3 a^{2} - 5)$

Apply the distributive property.

$- 8 a^{2} (3 a^{2}) - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 8 \cdot 3 a^{2} a^{2} - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$- 8 \cdot 3 (a^{2} a^{2}) - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 8 \cdot 3 a^{2 + 2} - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Add $2$ and $2$ .

$- 8 \cdot 3 a^{4} - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Multiply $- 8$ by $3$ .

$- 24 a^{4} - 8 a^{2} \cdot - 5 - 1 (3 a^{2}) - 1 \cdot - 5$

Multiply $- 5$ by $- 8$ .

$- 24 a^{4} + 40 a^{2} - 1 (3 a^{2}) - 1 \cdot - 5$

Multiply $3$ by $- 1$ .

$- 24 a^{4} + 40 a^{2} - 3 a^{2} - 1 \cdot - 5$

Multiply $- 1$ by $- 5$ .

$- 24 a^{4} + 40 a^{2} - 3 a^{2} + 5$

Subtract $3 a^{2}$ from $40 a^{2}$ .

$- 24 a^{4} + 37 a^{2} + 5$